Characterization of nonlinearity in servo patterns

ABSTRACT

A method according to one embodiment includes applying a static head skew to a magnetic tape head, positioning the first reader at a first y-position relative to a servo pattern in a servo band, and measuring y-positions of the second reader relative to the servo pattern in the servo band while the first reader is at the first y-position. A y-position value is calculated for the second reader based on the measured y-positions. The following process is repeated several times: moving the first reader to a next y-position, measuring y-positions of the second reader while the first reader is at the next y-position, and calculating a y-position value of the second reader based on the measured y-position of the second reader. A unique nonlinearity value of the servo pattern in the servo band is calculated for each of the calculated y-position values of the second reader.

BACKGROUND

The present invention relates to tape storage systems, and morespecifically, to linearity/nonlinearity of servo patterns.

Timing-based servo (TBS) is a technology which was developed for lineartape drives in the late 1990s. In TBS systems, recorded servo patternsinclude transitions with two different azimuthal slopes, thereby forminga chevron-type pattern. These patterned transitions allow for anestimate of the head lateral position to be determined by evaluating therelative timing of pulses generated by a servo reader reading thepatterns as they are passed over the servo reader.

In a TBS format, the servo pattern is prerecorded in several bandsdistributed across the tape. Typically, five or nine servo pattern bandsare included on a given tape which runs about parallel to a longitudinalaxis of the tape. Data is recorded in the regions of tape locatedbetween pairs of the servo bands. In read/write heads of lineartape-open (LTO) and IBM Enterprise tape drives, two servo readers arenormally available per head module, from which longitudinal position(LPOS) information as well as a position error signal (PES) may bederived. Effective detection of the TBS patterns is achieved by asynchronous servo channel employing a matched-filterinterpolator/correlator, which ensures desirable filtering of the servoreader signal.

With the increase in track density that is envisioned for future tapemedia and tape drives, accurately controlling the lateral position ofthe head and/or skew of the head with respect to tape by using feedbackgenerated by reading the TBS patterns becomes increasingly difficult.Conventional servo based implementations may not be sufficientlyaccurate to ensure adequate positioning of the data readers and writersthat move along data tracks. Furthermore, the repetition rate of thehead lateral position estimates may be too low to ensure propertrack-following operation as tape velocity varies during use. Therepetition rate of the head lateral position estimates may additionallybe unable to support future actuators with larger bandwidths.

SUMMARY

A method according to one embodiment includes applying a static headskew to a magnetic tape head for misaligning first and second readers ina direction perpendicular to a tape travel direction thereacross. Themethod further includes positioning the first reader at a firsty-position relative to a servo pattern in a servo band, and measuringy-positions of the second reader relative to the servo pattern in theservo band while the first reader is at the first y-position. Ay-position value is calculated for the second reader based on themeasured y-positions. The method further includes repeating thefollowing process several times: moving the first reader to a nexty-position, measuring y-positions of the second reader while the firstreader is at the next y-position, and calculating a y-position value ofthe second reader based on the measured y-position of the second readerwhile the first reader is at the next y-position. A unique nonlinearityvalue of the servo pattern in the servo band is calculated for each ofthe calculated y-position values of the second reader using therespective calculated y-position value of the second reader. The methodfurther includes storing and/or outputting the calculated nonlinearityvalues.

A computer program product for characterizing nonlinearity in atiming-based servo pattern according to one embodiment includes acomputer readable storage medium having program instructions embodiedtherewith. The program instructions are readable and/or executable by acontroller to cause the controller to perform the foregoing method.

An apparatus according to another embodiment includes a controllerconfigured to perform the foregoing method.

Other aspects and embodiments of the present invention will becomeapparent from the following detailed description, which, when taken inconjunction with the drawings, illustrate by way of example theprinciples of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a network storage system, according to oneembodiment.

FIG. 2 illustrates a simplified tape drive of a tape-based data storagesystem, according to one embodiment.

FIG. 3 illustrates a tape layout, according to one embodiment.

FIG. 4A shows a hybrid servo pattern written in a dedicated area of atape medium, according to one embodiment.

FIG. 4B shows a partial detailed view of a TBS pattern, according to oneembodiment.

FIG. 4C shows graph plotting sample vs. amplitude of the TBS pattern ofFIG. 4B, according to one embodiment.

FIG. 5A is a High-Density (HD) pattern, according to one embodiment.

FIG. 5B is a graph plotting readback energy vs. frequency for the readerin FIG. 5A.

FIG. 5C is a HD pattern, according to one embodiment.

FIG. 5D is a graph plotting readback energy vs. frequency for the readerin FIG. 5C.

FIG. 6 shows a block diagram of a detector for HD patterns, according tothe prior art.

FIG. 7 shows a block diagram of a detector for HD patterns, according toone embodiment.

FIG. 8 shows a first TBS pattern with linear servo bands, and a secondTBS pattern with nonlinear servo bands, according to one embodiment.

FIG. 9 shows a flowchart of a method, according to one embodiment.

FIG. 10A shows a magnetic tape head in a starting y-position relative toa servo pattern in a servo band, according to one embodiment.

FIG. 10B shows the magnetic tape head of FIG. 10A in an endingy-position relative to the servo pattern in the servo band.

FIG. 11A shows a graph plotting measured y-positions vs. linearizedy-positions, according to one embodiment.

FIG. 11B shows a graph plotting the measured y-positions of FIG. 11A vs.calculated unique nonlinearity values.

FIG. 12 shows a graph plotting nonlinearities at different y-positionsof TBS patterns of a first servo band on a magnetic tape, according toone embodiment.

FIG. 13 shows a graph plotting nonlinearities at different y-positionsof a second TBS pattern on the same magnetic tape as that of FIG. 12.

FIG. 14 shows a graph plotting differential pattern nonlinearity betweenthe TBS patterns of the first servo band sampled in FIG. 12 and the TBSpatterns of the second servo band sampled in FIG. 13, at differenty-positions.

FIG. 15A shows a graph plotting a measured delta y-position between theservo bands sampled FIGS. 12-13, and the differential patternnonlinearity of FIG. 14.

FIG. 15B shows a graph plotting an averaged and smoothed estimate of thedelta y-position obtained from five sequential captures, and thedifferential pattern nonlinearity of FIG. 14.

DETAILED DESCRIPTION

The following description is made for the purpose of illustrating thegeneral principles of the present invention and is not meant to limitthe inventive concepts claimed herein. Further, particular featuresdescribed herein can be used in combination with other describedfeatures in each of the various possible combinations and permutations.

Unless otherwise specifically defined herein, all terms are to be giventheir broadest possible interpretation including meanings implied fromthe specification as well as meanings understood by those skilled in theart and/or as defined in dictionaries, treatises, etc.

It must also be noted that, as used in the specification and theappended claims, the singular forms “a,” “an” and “the” include pluralreferents unless otherwise specified.

The following description discloses several preferred embodiments ofmagnetic storage systems, as well as operation and/or component partsthereof for characterizing nonlinearity in servo patterns.

In one general embodiment, a method includes applying a static head skewto a magnetic tape head for misaligning first and second readers in adirection perpendicular to a tape travel direction thereacross,positioning the first reader at a first y-position relative to a servopattern in a servo band, measuring y-positions of the second readerrelative to the servo pattern in the servo band while the first readeris at the first y-position, and averaging the measured y-positions. Themethod further includes repeating the following process several times:moving the first reader to a next y-position, measuring y-positions ofthe second reader while the first reader is at the next y-position, andaveraging the y-positions measured by the second reader while the firstreader is at the next y-position. The method further includescalculating a unique nonlinearity value of the servo pattern in theservo band for each of the average y-position values using therespective average y-position value, and storing and/or outputting thecalculated nonlinearity values.

In another general embodiment, a computer program product forcharacterizing nonlinearity in a timing-based servo pattern includes acomputer readable storage medium having program instructions embodiedtherewith. The computer readable storage medium is not a transitorysignal per se. The program instructions are readable and/or executableby a controller to cause the controller to perform the foregoing method.

In another general embodiment, an apparatus includes a controller. Thecontroller is configured to apply a static head skew to a magnetic tapehead for misaligning first and second readers in a directionperpendicular to a tape travel direction thereacross, position the firstreader at a first y-position relative to a servo pattern in a servoband, measure y-positions of the second reader relative to the servopattern in the servo band while the first reader is at the firsty-position, and average the measured y-positions. The controller isfurther configured to repeat the following process several times: movethe first reader to a next y-position, measure y-positions of the secondreader while the first reader is at the next y-position, and average they-positions measured by the second reader while the first reader is atthe next y-position. The controller is further configured to calculate aunique nonlinearity value of the servo pattern in the servo band foreach of the average y-position values using the respective averagey-position value, and store and/or output the calculated nonlinearityvalues.

Referring now to FIG. 1, a schematic of a network storage system 10 isshown according to one embodiment. This network storage system 10 isonly one example of a suitable storage system and is not intended tosuggest any limitation as to the scope of use or functionality ofembodiments of the invention described herein. Regardless, networkstorage system 10 is capable of being implemented and/or performing anyof the functionality set forth herein.

In the network storage system 10, there is a computer system/server 12,which is operational with numerous other general purpose or specialpurpose computing system environments or configurations. Examples ofwell-known computing systems, environments, and/or configurations thatmay be suitable for use with computer system/server 12 include, but arenot limited to, personal computer systems, server computer systems, thinclients, thick clients, handheld or laptop devices, multiprocessorsystems, microprocessor-based systems, set top boxes, programmableconsumer electronics, network PCs, minicomputer systems, mainframecomputer systems, and distributed cloud computing environments thatinclude any of the above systems or devices, and the like.

Computer system/server 12 may be described in the general context ofcomputer system-executable instructions, such as program modules, beingexecuted by a computer system. Generally, program modules may includeroutines, programs, objects, components, logic, data structures, and soon that perform particular tasks or implement particular abstract datatypes. Computer system/server 12 may be practiced in distributed cloudcomputing environments where tasks are performed by remote processingdevices that are linked through a communications network. In adistributed cloud computing environment, program modules may be locatedin both local and remote computer system storage media including memorystorage devices.

As shown in FIG. 1, computer system/server 12 in the network storagesystem 10 is shown in the form of a general-purpose computing device.The components of computer system/server 12 may include, but are notlimited to, one or more processors or processing units 16, a systemmemory 28, and a bus 18 that couples various system components includingsystem memory 28 which is coupled to processor 16.

Bus 18 represents one or more of any of several types of bus structures,including a memory bus or memory controller, a peripheral bus, anaccelerated graphics port, a processor or local bus using any of avariety of bus architectures, etc. By way of example, which is in no wayintended to limit the invention, such architectures include IndustryStandard Architecture (ISA) bus, Micro Channel Architecture (MCA) bus,Enhanced ISA (EISA) bus, Video Electronics Standards Association (VESA)local bus, and Peripheral Component Interconnects (PCI) bus.

Computer system/server 12 typically includes a variety of computersystem readable media. Such media may be any available media that isaccessible by computer system/server 12, and may include both volatileand non-volatile media, removable and non-removable media.

System memory 28 may include computer system readable media in the formof volatile memory, such as random access memory (RAM) 30 and/or cachememory 32. Computer system/server 12 may further include otherremovable/non-removable, volatile/non-volatile computer system storagemedia. By way of example only, storage system 34 may be provided forreading from and writing to a non-removable, non-volatile magneticmedia—not shown and typically called a “hard disk,” which may beoperated in a hard disk drive (HDD). Although not shown, a magnetic diskdrive for reading from and writing to a removable, non-volatile magneticdisk (e.g., a “floppy disk”), and an optical disc drive for reading fromor writing to a removable, non-volatile optical disc such as a compactdisc read-only memory (CD-ROM), digital versatile disc-read only memory(DVD-ROM) or other optical media may be provided. In such instances,each disk drive may be connected to bus 18 by one or more data mediainterfaces. As will be further depicted and described below, memory 28may include at least one program product having a set (e.g., at leastone) of program modules that are configured to carry out the functionsof embodiments described herein.

Program/utility 40, having a set (at least one) of program modules 42,may be stored in memory 28 by way of example, and not limitation, aswell as an operating system, one or more application programs, otherprogram modules, program data, etc. Each of the operating system, one ormore application programs, other program modules, and program data orsome combination thereof, may include an implementation of a networkingenvironment. It should also be noted that program modules 42 may be usedto perform the functions and/or methodologies of embodiments of theinvention as described herein.

Computer system/server 12 may also communicate with one or more externaldevices 14 such as a keyboard, a pointing device, a display 24, etc.;one or more devices that enable a user to interact with computersystem/server 12; and/or any devices (e.g., network card, modem, etc.)that enable computer system/server 12 to communicate with one or moreother computing devices. Such communication may occur via Input/Output(I/O) interfaces 22. Still yet, computer system/server 12 maycommunicate with one or more networks such as a local area network(LAN), a general wide area network (WAN), and/or a public network (e.g.,the Internet) via network adapter 20. As depicted, network adapter 20communicates with the other components of computer system/server 12 viabus 18. It should be understood that although not shown, other hardwareand/or software components could be used in conjunction with computersystem/server 12. Examples, include, but are not limited to: microcode,device drivers, redundant processing units, external disk drive arrays,redundant array of independent disks (RAID) systems, tape drives, dataarchival storage systems, etc.

Looking to FIG. 2, a tape supply cartridge 120 and a take-up reel 121are provided to support a tape 122. One or more of the reels may formpart of a removable cartridge and are not necessarily part of the tapedrive 100. A tape drive, e.g., such as that illustrated in FIG. 2, mayfurther include drive motor(s) to drive the tape supply cartridge 120and the take-up reel 121 to move the tape 122 over a tape head 126 ofany type. Such head may include an array of readers, writers, or both.

Guides 125 guide the tape 122 across the tape head 126. Such tape head126 is in turn coupled to a controller 128 via a cable 130. Thecontroller 128, may be or include a processor and/or any logic forcontrolling any subsystem of the drive 100. For example, the controller128 may control head functions such as servo following, data writing,data reading, etc. The controller 128 may include at least one servochannel and at least one data channel, each of which include data flowprocessing logic configured to process and/or store information to bewritten to and/or read from the tape 122. The controller 128 may operateunder logic known in the art, as well as any logic disclosed herein, andthus may be considered as a processor for any of the descriptions oftape drives included herein according to various embodiments. Thecontroller 128 may be coupled to a memory 136 of any known type, whichmay store instructions executable by the controller 128. Moreover, thecontroller 128 may be configured and/or programmable to perform orcontrol some or all of the methodology presented herein. Thus, thecontroller 128 may be considered to be configured to perform variousoperations by way of logic programmed into one or more chips, modules,and/or blocks; software, firmware, and/or other instructions beingavailable to one or more processors; etc., and combinations thereof.

The cable 130 may include read/write circuits to transmit data to thehead 126 to be recorded on the tape 122 and to receive data read by thehead 126 from the tape 122. An actuator 132 controls position of thehead 126 relative to the tape 122.

An interface 134 may also be provided for communication between the tapedrive 100 and a host (internal or external) to send and receive the dataand for controlling the operation of the tape drive 100 andcommunicating the status of the tape drive 100 to the host, all as willbe understood by those of skill in the art.

Referring momentarily to FIG. 3, an illustrative tape layout is depictedin accordance with one embodiment. As shown, tape 300 has a tape layoutwhich implements five servo bands Servo Band 0-Servo Band 4, and fourdata bands Data Band 0-Data Band 3, as specified in the LTO format andIBM Enterprise format. The height H of each of the servo bands ismeasured in the cross-track direction 304 which is about orthogonal tothe length L of the tape 300. According to an example, the height H ofeach of the servo bands may be about 186 microns according to the LTOformat. Moreover, a pitch β between the servo bands as shown may beabout 2859 microns, again according to the LTO format.

An exemplary tape head 302 is also shown as having two modules and asbeing positioned over a portion of the tape 300 according to oneapproach. Read and/or write transducers may be positioned on eithermodule of the tape head 302 according to any of the approaches describedherein, and may be used to read data from and/or write data to the databands. Furthermore, tape head 302 may include servo readers which may beused to read the servo patterns in the servo bands according to any ofthe approaches described herein. It should also be noted that thedimensions of the various components included in FIG. 3 are presented byway of example only and are in no way intended to be limiting.

Some tape drives may be configured to operate at low tape velocitiesand/or with nanometer head position settings. These tape drives may useservo formats that target Barium Ferrite (BaFe) tape media, 4 or 8 databands, 32 or 64 data channel operation, allow very low velocityoperation, support large-bandwidth actuator operation, and improveparameter estimation to minimize standard deviation of the positionerror signal (PES), thus enabling track-density scaling for tapecartridge capacities up to 100 TB and beyond.

However, according to some embodiments, magnetic tape may further beaugmented with additional features that provide additionalfunctionality. Accordingly, HD servo patterns may be implemented inplace of the standard TBS patterns, e.g., as seen in FIG. 3. The HDservo patterns may be used to improve track-following performance.

In still further embodiments, a standard TBS pattern (e.g., as shown inFIG. 3) may be implemented in combination with one or more HD servopatterns (e.g., see FIG. 4A below). One implementation includes a hybridservo pattern scheme, in which a standard TBS pattern is retained andadditional HD patterns are provided in a dedicated, preferably currentlyunused area of the tape media. This type of pattern may be implementedby increasing the number of data channels from 16 to 32, and reducingthe width of the TBS pattern from 186 microns to 93 microns, in someapproaches.

A hybrid servo pattern 410, which includes a standard TBS pattern 402written in a servo band, as well as an HD pattern 404 that is written ina HD band (e.g., dedicated area) of the tape medium 408 is shown in FIG.4A. Moreover, each HD pattern 404 includes a number of HD tracks, eachof the HD tracks having a respective periodic waveform, e.g., as seen inFIGS. 5A, 5C and 11A below. In some approaches, significant features ofthe original TBS pattern 402 are retained, such as a servo framestructure consisting of four servo bursts containing a number of servostripes, where the servo stripes of adjacent servo bursts are writtenwith alternating azimuthal angle. Other parameters of legacy servopatterns, such as the servo pattern height and other geometricdimensions, as well as the number of servo stripes per burst, may bemodified as desired.

The HD pattern 404 may include periodic waveforms of various frequenciesalternately written in the length direction L along a longitudinal axisof the tape. The standard TBS pattern 402 may be used to provide initialidentification of the servo band (e.g., by providing a servo band ID);initial positioning of the head 406 on an appropriate servo location;acquisition of initial servo channel parameters, such as tape velocity,lateral head position, head-to-tape skew, longitudinal position (LPOS),etc.; etc. Moreover, the HD pattern 404 may enable more accurate andmore frequent estimates of servo channel parameters, thereby achievingimproved head positioning at a much wider range of tape velocities andsupport for larger bandwidth head actuation. As such, track-densityscaling may be enabled for very large cartridge capacities, as well asimproved data rate scaling with host computer requirements through thesupport of a wider velocity range.

The detection of the periodic waveforms forming a HD pattern may beobtained by a detector that implements a complex algorithmic conversion,e.g., such as a Discrete Fourier Transform (DFT), a Fast FourierTransform (FFT), etc. However, this implementation complexity may reducethe flexibility in trade-offs between the rate of generation of servoreader lateral position estimates and the standard deviation of theestimation error. Accordingly, components (e.g., controllers) with highthroughput may desirably be used to process signals derived from a HDpattern in order to reduce the processing time thereof.

In one embodiment, a detector capable of reading a hybrid of TBS and HDpatterns may be implemented. The hybrid detector may be configured toobtain estimates of the energy of relevant spectral frequency componentsin a readback signal from the HD pattern, while also calculatingestimates of the lateral position of the head based on these energies,without applying a DFT or a FFT.

Samples provided at the input of the components performing the spectralestimation may be obtained at the proper sampling instants byinterpolating the sequence of readback HD servo signal samples from ananalog-to-digital (A/D) converter at a fixed clock frequency in oneembodiment, or at a variable clock frequency in another embodiment. Thetime base of the interpolator may be derived from the estimate of thetape velocity provided by the TBS channel operating in parallel with theHD detector, in some embodiments, as will be described in further detailbelow.

Various trade-offs between the rate of generation of spectral estimates,from which servo reader lateral position estimates are obtained, and thestandard deviation of the estimation error are possible. However, asuitable and preferred implementation may be achieved with asignificantly reduced complexity compared to DFT-based or FFT-basedimplementations. Specifically, in one embodiment, only a small set ofspectral estimates are computed, compared to the fixed set ofequally-spaced spectral components computed by a DFT or FFT.Furthermore, the integration interval may be freely adjusted, while aDFT/FFT-based solution involves the integration interval being multiplesof the DFT/FFT size.

Even when the HD servo pattern uses a large number of tone frequencies,the maximum number of spectral estimates that are computed by theproposed detector may correspond to the maximum number of tracks that anHD servo reader reads simultaneously at any time. Also, the proposeddetector may be reconfigured to provide spectral estimates correspondingto the tracks currently being read based on the coarse positioninginformation from the TBS channel.

Referring again to FIG. 4A, which shows a tape layout 400 with a hybridservo pattern 410 according to one embodiment, in the hybrid servopattern 410, an HD pattern 404 is written in a space adjacent to astandard TBS pattern 402. According to the present embodiment,quadrature sequences are not included due to the use of the TBS pattern402, which is converse to products implementing servo functionality inhard-disk drives.

Looking momentarily to FIG. 4B, a partial detailed view of a TBS pattern402 (e.g., a TBS frame) is illustrated according to an exemplaryembodiment. As shown, a plurality of servo stripes 412 together form aservo burst 414, while corresponding pairs of servo bursts 414 formservo sub-frames. Accordingly, the depicted TBS frame has four servobursts 414 and two servo sub-frames. In the present embodiment, theservo bursts 414 included in the left servo sub-frame each have fiveservo stripes 412, while the servo bursts 414 included in the rightservo sub-frame each have four servo stripes 412. The servo stripes 412included in a given servo burst 414 are oriented such that they have asame azimuthal slope represented by angle α. Moreover, correspondingpairs of servo bursts 414 have opposing azimuthal slopes, therebyforming a chevron-type pattern. The height H and thickness t of theservo stripes 412 may vary depending on the servo writer used to writethe TBS pattern 402. According to an exemplary approach, which is in noway intended to limit the invention, the height H may be about 186 μm,and the angle α may be about 6°, while the thickness t is about 2.1 μm.Moreover, the spacing S between each of the servo stripes 412 and/or thedistance d between servo bursts 414 having the same azimuthal slope mayvary depending on the desired embodiment. According to an exemplaryapproach, which is in no way intended to limit the invention, thespacing S may be about 5 μm, while the distance d is about 100 μm. Asdescribed above, patterned transitions such as that shown in FIG. 4Ballow for an estimate of the head lateral position to be determined byevaluating the relative timing of pulses generated by a servo readerreading the servo stripes 412 of the servo burst 414 as they are passedover the servo reader.

Referring again to FIG. 4A, the HD pattern 404 may include periodicwaveforms written on adjacent tracks. For example, two periodicwaveforms, characterized by two different spatial frequencies:low-frequency f₁ and high-frequency f₂, where f₂>f₁. However, a widerrange of lateral head displacement is desired. Accordingly, a differentconfiguration of the HD patterns may be used to avoid ambiguity indetermining the lateral displacement.

FIG. 4C illustrates a graph 418 plotting sample vs. amplitude of the TBSpattern 402 of FIG. 4B, detected as a servo readback signal 416 duringreadback. A servo channel may decode the readback signal that isreceived from a servo reader of a magnetic tape head reading the TBSpattern 402. For example, when a servo stripe 412 of the TBS pattern 402passes across the servo sensor, a double pulse portion 420 (having apositive peak and a negative peak) of the readback signal 416 isgenerated, e.g., for purposes of an example see lateral dashed linesindicating how double pulse portions of the readback signal 416correspond to servo stripe read locations. Accordingly, two or more ofsuch double pulse portions and timing associated therewith may be usedin calculating lateral position (y-position) estimates.

In one approach, the servo channel may provide y-position estimates to atrack-following control system, e.g., where such y-position estimatesare calculated using Equation 1 below.

$\begin{matrix}{\hat{y} = {\frac{d}{2\; {\tan (\alpha)}}\left( {\frac{1}{2} - \frac{\sum A_{i}}{\sum B_{i}}} \right)}} & {{Equation}\mspace{14mu} 1}\end{matrix}$

As shown above, the lateral y-position estimate ŷ of Equation 1 mayincorporate: the distance d, the azimuthal slope (angle α) of the servostripes 412, a measured time B_(i) between pairs of corresponding servostripes with the same azimuth angle (e.g., parallel stripes //, or \\)from two different sub-frames, and a measured time A_(i) between pairsof corresponding servo stripes with opposite azimuth angle (e.g.,stripes /\) from the same sub-frame.

For example, in the 5-5-4-4 pattern of FIG. 4C, four measurements A_(i),i=0, 1, 2, 3 and four measurements of B_(i), i=0, 1, 2, 3 are performedper servo sub-frame of the TBS pattern 402 of FIG. 4B. In someapproaches, the distance d is may be referred to as the “sub-framelength.”

An HD servo pattern preferably includes periodic waveforms of differingfrequencies alternately written in the lateral (cross-track) direction.Accordingly, HD servo patterns may be able to desirably provide moreaccurate and/or more frequent estimates of servo channel parametersaccording to various embodiments described herein. Looking to FIGS.5A-5D, an HD pattern 500 is shown that overcomes the limited range oflateral head displacement associated with an HD pattern having only twoperiodic waveforms, characterized by two different spatial frequencies.As shown in FIGS. 5A and 5C, at least three frequencies are used for theHD pattern 500 in adjacent tracks, which repeat periodically across theband where the HD pattern is written. In the embodiment of FIGS. 5A and5C, the servo reader (denoted by the block labelled ‘R’) spans wider inthe cross-track direction 502 than a single track, such that at leasttwo tones/frequencies are detected under any reading conditions at agiven time when the servo reader R is overlapped with the HD pattern500. Looking specifically to FIG. 5A, the reader R spans across both thebottom portion 508 and middle portion 506 of the HD pattern 500. FIG. 5Cillustrates an alternative position for the servo reader R, where thereader R spans across the upper portion 504 and middle portion 506 ofthe HD pattern 500.

The three portions 508, 506, 504 of the periodic waveforms arecharacterized by three different frequencies f₁, f₂, and f₃,respectively, where f₃>f₂>f₁. According to various approaches, eachwaveform may be characterized as having a number of periods in a rangefrom about 25 to about 200, such as 30 periods, 50 periods, 75 periods,100 periods, etc., within a predetermined spacing. More preferably, thepredetermined spacing may be in a range from about 50 μm to about 150μm, such as about 60 μm, about 75 μm, about 100 μm, etc., depending onthe approach. Moreover, the symbol length may be in a range from about0.5 μm to about 3.0 μm, e.g., such as about 1.0 μm, about 1.5 μm, about2.0 μm, etc.

Hence, with continued reference to FIGS. 5A-5D, an edge of one of theportions of the HD pattern 500 may be distinguished from the edge ofanother of the portions. Looking specifically to FIG. 5A, an edge of themiddle portion 506 may be distinguished from an edge of the bottomportion 508 by evaluating the signals read by the servo reader R, whichoverlaps both portions 506, 508. The graph 510 in FIG. 5B identifies thevarious frequencies in the readback signal from servo reader R and theenergy level corresponding to each of the respective frequencies for theposition of the servo reader R shown in FIG. 5A. Energy values may bedetermined in some approaches by integrating over a given amount of time(or distance along the tape). As shown in graph 510, in addition to themiddle frequency f₂, the bottom frequency f₁ is present in the readbacksignal of the servo reader R and may thereby be detected by a spectralanalysis. Furthermore, the energy values of the spectral components f₁and f₂ represent the relation of the servo reader R overlapping themiddle and bottom portions 506, 508. Given that the energy value of thespectral component of frequency f₁ is smaller than the energy value ofthe spectral component of the second frequency f₂, it follows that theservo reader R can be determined to be overlapped with the middleportion 506 more than it is overlapped with the bottom portion 508.Moreover, a comparison of the corresponding energies may be used todetermine a fine position of the servo reader R with respect to amagnetic tape.

Similarly, the graph 520 in FIG. 5D identifies the frequencies in thereadback signal from servo reader R positioned as shown in FIG. 5C, aswell as the energy level corresponding to each of the respectivefrequencies. As shown, frequencies f₂, and f₃ are present in thereadback signal of the servo reader R, and may be detected by a spectralanalysis. Again, the energies of the spectral components for frequenciesf₂, and f₃ indicate that the servo reader R is positioned above theupper and middle portions 504, 506. Given that the energy of thespectral component of frequency f₃ is smaller than the energy of thespectral component of frequency f₂, it follows that the servo reader Ris overlapped with the middle portion 506 more than it is overlappedwith the upper portion 504. Moreover, a comparison of the correspondingenergy values may be used to determine a fine position of the servoreader R with respect to a magnetic tape.

Note that the waveform periods of the three frequencies may be integermultiples of a period T, for example T=241.3 nm, which corresponds tothe highest spatial frequency, which is proportional to 1/T, whenspectral estimation by a DFT/FFT-based detector with a minimum number ofspectral bins for given integration interval is adopted.

FIG. 6 shows a block diagram of a DFT/FFT-based detector 600 configuredfor the computation of the PES from an HD servo pattern comprisingperiodic waveforms. The servo signal from the servo reader 602 isinterpolated using a servo signal interpolator 604 with the timinginformation from a synchronous servo channel 606. The interpolatedsignal samples are then processed by either a DFT-based or a FFT-based(DFT/FFT-based) detector 608 that estimates the signal energy values atfrequencies f₁ and f₂. The DFT/FFT-based detector 608 outputs are inputto a PES computation unit 610, which determines a PES estimate by takingthe difference of the signal energy values.

Ideally, the two periodic waveforms, whose energies are estimated by theDFT/FFT-based detector 608, are sinusoidal waveforms at frequencies f₁and f₂. However, a DFT/FFT-based detector 608 when used for HD patternshas an inherent drawback where the number of spectral components, forwhich an estimate of the energy is provided, depends on the integrationinterval for the DFT (or FFT) computation, and may be very large whenthe integration interval extends over several periods of the fundamentalfrequency, as is typically the case when a low-noise estimation processis used.

As the number of periodic waveform components forming the readbacksignal of an HD pattern is usually limited to two or three for a givenlateral position, it is advantageous to resort to a low-complexityimplementation of the detector, whereby only estimates of the energy ofthe relevant spectral components at two or three frequencies in thereadback signal of an HD pattern are efficiently computed.

Now referring to FIG. 7, a detector 700 for HD patterns is shownaccording to one embodiment. The detector 700 is configured to operatewith periodic waveforms, which correspond to the components of thereadback signal of an HD pattern, that are characterized by threefrequencies at any time, as illustrated for example in FIGS. 5A-5Baccording to one embodiment. With continued reference to FIG. 7, thedetector 700 includes three digital filters 702, 704, 706 with lowimplementation complexity, each digital filter comprising a second-orderinfinite impulse response (IIR) stage followed by a two-tap finiteimpulse response (FIR) stage, for the estimation of the energy of thereadback HD servo signal at a specific frequency according to theGoertzel algorithm. Other arrangements and components may be used forthe three digital filters 702, 704, 706 as would be understood by one ofskill in the art upon reading the present descriptions. The waveformperiods (in nm) corresponding to the three frequencies may be assumed tobe integer multiples of a fundamental period, T.

For an accurate estimation of the energies of the three periodicwaveform components in a finite integration interval, the frequencies ofthe periodic waveform components preferably match the characteristicfrequencies of the three digital filters 702, 704, 706, denoted byω₀/2π, ω₁/2π, and ω₂/2π, respectively. When a match is not possible, itis preferred that the frequencies are within about 0.001% to 1.0% of thefrequencies set for the three digital filters 702, 704, 706, and morepreferably a difference of less than about 0.1%. This may be achieved byresampling the output sequence of the analog-to-digital converter (ADC)708 at appropriate time instants, which may be provided by aninterpolator 710, with a time base obtained from the tape velocity and agiven interpolation distance Δx_(HD), as shown in FIG. 7. The frequencyf_(s) of the clock 718, is used as an input to the ADC 708, the counter720, and the digital circuitry of the detector 700. Moreover thefrequency f_(s) of the clock 718 may be either a fixed frequency or avariable frequency.

In one embodiment, the interpolator 710 may be a cubic Lagrangeinterpolator to achieve smaller signal distortion than a linearinterpolator. Of course, any suitable interpolator may be used, as wouldbe understood by one of skill in the art. The output signal samples ofthe interpolator 710 are obtained that correspond with HD servo signalsamples taken at points on the tape that are separated by a stepinterpolation distance equal to Δx_(HD), independently of the tapevelocity. Δx_(HD) is preferably selected such that the conditionT/Δx_(HD)=K is satisfied independently of the tape velocity, where K isa positive integer number. The time base for the generation of theinterpolator output samples may be provided by an interpolation timecomputation unit 712, which yields the sequence of time instants{t_(n)}, at which the resampling of the ADC output sequence takes place.Time instants {t_(n)} may furthermore be provided to circular buffer722.

The detector 700 illustrated in FIG. 7 may be configured such that agiven number of samples is computed by the interpolator 710 within aclock interval T_(s)=1/f_(s). However, doing so may set a limit on themaximum tape velocity at which the detector 700 may operate, the maximumtape velocity represented by 2Δx_(HD)/T_(s). The maximum tape velocitysupported by the detector 700 may be increased by allowing a largernumber of samples to be computed by the interpolator 710 within a singleclock interval, but doing so also increases computational complexity.

For a fixed tape velocity, the time instants {t_(n)} may be uniformlyspaced by T_(I) seconds, where T_(I) denotes the time interval that ittakes for the tape to travel over a distance equal to the stepinterpolation distance Δx_(HD). The estimation of the time intervalT_(I) is performed by a step interpolation time computation unit 714,which computes T_(I)=Δx_(HD)/ν_(est), i.e., the ratio between Δx_(HD)and the estimate of the instantaneous tape velocity ν_(est), which maybe obtained from the TBS channel in one approach. The TBS channel mayoperate as a synchronous TBS channel according to one embodiment. Theaverage number of interpolated signal samples generated per ADC clockinterval is given by the ratio T_(I)/T_(s), where T_(s)=1/f_(s) denotesthe clock interval. The ADC clock frequency, f_(s), may be a fixedfrequency in one approach, or a variable frequency in another approach.

In one embodiment, the HD detector 700 may be configured to estimate thetape velocity to determine time instants at which to obtain interpolatedsignal samples to input to the Goertzel algorithm as filtering elementsbased on an output of a TBS channel of the tape drive configured toprocess a TBS pattern written on the servo band of the magnetic tapemedium.

In another embodiment, the HD detector 700 may be configured to computea head lateral position estimate for coarse positioning of the servoreader based on an output of a TBS channel of the tape drive. Also, theHD detector 700 may be configured to adjust settings for at least onedigital filter according to waveform frequency components of the HDservo signal estimated based on the head lateral position estimate. Forexample, the setting ω_(i) of the i-th digital filter may be adjustedbased on the coarse position estimate and the known frequencyω_(i)=2πf_(i) of the HD patterns located at that estimated (coarse)lateral position. In another example, the settings of the i-th digitalfilter may be adjusted based on the coarse position estimate and thecombination of symbol length, integration interval, etc., of the HDpatterns located at that estimated (coarse) lateral position.

The HD detector 700 receives, as inputs, values of the threecharacteristic frequencies {ω₀, ω₁, ω₂}, with ω_(i)=2πf_(i) from whichthe coefficients of the digital filters 702, 704, 706 are obtained.These frequencies may be obtained from the knowledge of the servo readerlateral position provided by the TBS channel in one embodiment, asdescribed above. Assuming the number “Q” represents the number ofsamples over which the estimates of the energies of the periodicwaveforms are computed, Q may determine the length of the integrationinterval, and therefore may also determine the spatial frequencyresolution. Assuming the value of Q is even, Q/2 represents the numberof frequencies for which energy estimates would be provided by aDFT/FFT-based HD detector that operates over Q samples. Q may beobtained from the tape drive memory in one embodiment. Moreover, Q istypically about 100 or larger.

Multiplication of the three energy estimates by gain factors g_(i), fori=0, 1, 2, is provided to compensate for the different attenuations thatthe readback HD servo signal may experience at different frequencies,where the normalization g₁=1 may be assumed. Hence, a lateral positionestimate of the HD servo reader 716, and hence a position error signalfrom the knowledge of the target head position, may be obtained by alinear combination of the three energy estimates. Note that the maximumnumber of spectral estimates that are computed at any time is determinedby the maximum number of tracks that may be read by the HD servo reader716, which may equal three in some approaches, and not by the overallnumber of tones in the HD servo pattern, which may be larger than three.In a case where the number of tones is larger than three, the values ofthe three characteristic frequencies {ω₀, ω₁, ω₂} that are provided tothe HD detector 700 may be derived from knowledge of the lateralposition estimate obtained from the TBS channel, as mentioned above.

In another embodiment, the HD detector 700 may be implemented without aninterpolator 710, but with digital filters configurable to adjust theirsettings according to the waveform spatial frequency components of theHD servo signal read from the magnetic tape medium and the tapevelocity. Adjustment of the digital filters settings may be based on acoarse head lateral position estimate and/or a tape velocity estimatecomputed based on an output of a TBS channel of the tape drive.

In an alternate embodiment, an HD detector may implement additionaldigital filters, in excess to the digital filters used to estimate theenergies at the frequencies corresponding to the patterns written on thetracks being read simultaneously by the HD servo reader 716. The one ormore excess digital filters may be used to simplify reconfiguration ofthe detector when the target lateral position changes and, therefore,the input values of frequencies {ω_(x)} vary dynamically.

In a further embodiment, the one or more excess digital filters may beused to distinguish HD patterns characterized by a small number ofspectral components/lines from broadband noise and/or data signals. Thismay be achieved by choosing the characteristic frequency ω_(i) of theexcess digital filter such that it measures a spectral component at afrequency that is not used by the HD patterns.

The outputs |X_(i,t)|² from the three digital filters 702, 704, 706 areprovided to a PES computation unit 724, which provides a position errorestimate (ε_(t)) at given time t.

Other components of the HD detector 700 may operate as would be known toone of skill in the art, and are omitted here for the sake of clarity ofthe described embodiments.

Linear magnetic tape recording systems often utilize TBS patterns toestimate head lateral position. During tape drive operation, amagneto-resistive servo read transducer in the head scans over the TBSpattern and a readback signal is produced, e.g., see FIG. 4C. A servochannel processes the servo readback signal and measures the timeintervals between bursts of stripes/dibits to estimate the tape headlateral position (y-position) relative to the TBS pattern. Aposition-error signal (PES) is generated by subtracting the estimatedhead position from the desired lateral position/trajectory and providedto a servo controller. The servo controller, in combination with acurrent driver and a head actuator, adjusts the position of the head andthereby closes the track-following servo control loop.

The y-position may be estimated from the TBS patterns by measuring thetime between the A-burst and B-burst stripes (and between C-burst andD-burst stripes), also termed as A-counts (A_(i)). Specifically, they-position is linearly dependent on the A-count values (A_(i)), providedthat the servo stripes are perfectly “straight”. For example, in the5-5-4-4 servo pattern of FIGS. 4B-4C, the bursts of stripes/////\\\\\////\\\\ correspond to the A B C D-burst, respectively. i.e.,A-burst=/////, B-burst=\\\\\, C-burst=////, D-burst=\\\\.

However, servo stripes that are factory pre-formatted on tape cartridgesare often not perfectly “straight”, e.g. due to manufacturingimperfections or defects in the servo writer. This leads to a non-linearrelationship between measured y-positions, e.g., based on A_(i)measurements (see FIG. 4C), and actual (true) y-positions of the head.

For example, referring to FIG. 8, representation 800 includes two TBSpatterns 802, 806. The TBS pattern 802 is a linear pattern, with linearservo stripes 804. In some approaches, a TBS pattern may becharacterized as being “linear” or “straight” if A-count distancesA_(i1), A_(i2) of the TBS pattern 802 linearly increase as a function ofthe (y)-position of the intended trajectory of the servo reader. Forexample, the stripes 804 of the TBS pattern 802 appear relativelylinear/straight.

In contrast, where A-count distances of a TBS pattern do not linearlyincrease as a function of the (y)-position of the intended trajectory ofthe servo reader, the TBS pattern may be characterized as being anonlinear “curved” TBS pattern. For example, see nonlinear stripes 808of the TBS pattern 806, which will result in the A-count distancesA_(i3), A_(i4) not linearly increasing as a function of the (y)-positionof the intended trajectory of the servo reader. Accordingly, nonlinearTBS patterns may cause a data track to be written slightly offset (incross-track direction) from the desired location. The nonlinearity inthe TBS patterns therefore may cause some tracks to be wider or narrowerthan the nominal/desired width, which leads to more variability/degradedperformance when the data is read from magnetic tape. This is becausemeasured A-count distances will not entirely accurately reflect therelative position of the head with respect to servo bands and/or databands. As a result of such nonlinearities, data written to data tracksof the magnetic tape may be compressed or spaced too far apart.Accordingly, as a result of the TBS pattern 806 being nonlinear (up to ananometer degree), a y-position dependent error e may result.Specifically, the y-position dependent error e may result from adifference existing between an average measured y-position 810 and anactual (true) y-position 812. Note that in FIG. 8, in one approach, itmay be assumed that A_(i1)=A_(i3). Moreover, assuming that the truereader position is position 812, then based on the measured A_(i3)(=A_(i1)), and assuming that the servo pattern is linear, the “measured”y-position is y-position 810.

In various approaches, for each servo band/pattern, the intention is todetermine the y-position dependent error e, such that an estimate of theactual (true) y-position, which is referred to as linearized y-position,can be computed by subtracting the y-position dependent error e from themeasured y-position.

Various embodiments described herein characterize the nonlinearity inservo patterns. According to various embodiments, such nonlinearitycharacterizations are calculated and thereafter stored and/or used forcompensating for such nonlinearities, as will become apparent fromreading various descriptions herein.

It should be noted that such characterizations may be made on any typeof servo patterns, although many of the embodiments and/or approachesdescribed herein may specifically reference TBS patters. For example, inaddition and/or as an alternative to TBS patterns, embodiments and/orapproaches described herein may be applied to HD servo patterns (seeFIGS. 5A-5D).

Now referring to FIG. 9, a flowchart of a method 900 is shown accordingto one embodiment. The method 900 may be performed in accordance withthe present invention in any of the environments depicted in FIGS. 1-8,among others, in various embodiments. Of course, more or less operationsthan those specifically described in FIG. 9 may be included in method900, as would be understood by one of skill in the art upon reading thepresent descriptions.

Each of the steps of the method 900 may be performed by any suitablecomponent of the operating environment. For example, in variousembodiments, the method 900 may be partially or entirely performed by adrive controller, a host coupled to a drive, or some other device havingone or more processors therein. The processor, e.g., processingcircuit(s), chip(s), and/or module(s) implemented in hardware and/orsoftware, and preferably having at least one hardware component may beutilized in any device to perform one or more steps of the method 900.Illustrative processors include, but are not limited to, a centralprocessing unit (CPU), an application specific integrated circuit(ASIC), a field programmable gate array (FPGA), etc., combinationsthereof, or any other suitable computing device known in the art.

As shown in FIG. 9, method 900 includes operation 902, where a statichead skew is applied to a magnetic tape head for misaligning first andsecond readers in a direction perpendicular to a tape travel direction,e.g., direction of a magnetic recording tape thereacross. It should benoted that the amount of head skew applied to the magnetic tape head maydepend on the approach, as would become apparent to one of ordinaryskill in the art upon reading the descriptions of various embodimentsand/or approaches herein. As noted above, the head skew is static, i.e.,the skew angle does not change during performance of the method. Notethat changing the head skew during performance of the method andapplying a factor to compensate for the changed skew angle should beconsidered equivalent.

According to one approach, the static head skew is applied to themagnetic tape head by an actuator. Accordingly, operation 902 mayinclude instructing a skew actuator.

It should be noted that method 900 may be performed during any one ormore directions of tape travel, e.g., in a single direction of tapetravel, such as forward (beginning of tape to end of tape), or backward(end of tape to beginning of tape); or in both directions of tapetravel, such as forward and backward. However, in preferred approaches,method 900 is performed with the tape traveling in a single direction.

Operation 904 of method 900 includes positioning the first reader at afirst y-position relative to a servo pattern in a servo band. Asmentioned elsewhere herein, the servo pattern may be any type of servopattern. According to some approaches, the servo pattern is a TBSpattern that comprises bursts of servo stripes. According to some otherapproaches, the servo pattern is a HD servo pattern containing multipleHD tracks having a repeating periodic waveform.

The first y-position may be any position relative to a servo pattern ina servo band of the magnetic tape. In a preferred approach, the firsty-position is located toward an outermost lateral portion of the servopattern in a servo band of the magnetic tape. The first y-position maybe predefined, selected on the fly, etc.

Operation 906 of method 900 includes measuring y-positions of the secondreader relative to the servo pattern in the servo band while the firstreader is at the first y-position, e.g., while the first reader islocked to and track follows at the first y-position while the tape ismoving over the magnetic tape head. Any number of y-positions of thesecond reader may be measured, e.g., according to some predefinedcriteria. For example, according to various approaches, a y-position maybe computed, e.g., for each servo frame, for every other frame, forevery 5^(th) frame, etc.

In one approach, some or all of the measured y-positions are at leasttemporarily stored in memory, e.g., to be subsequently used in any typeof calculating.

In one approach, some or all of the measured y-positions of the secondreader are averaged, e.g., see operation 908. In one approach, they-positions are averaged each time a y-position measurement is performedby the second reader, while the first reader is at the first y-position.In another approach, the y-positions are averaged after all of they-position measurements are performed by the second reader at thecurrent y-position. In yet another approach, a subset of the measuredy-positions are selected for averaging based on predefined criteria suchas every other measured y-position, every 5^(th) measured y-position,y-position values within a range e.g., to exclude outliers, etc.

Operation 910 includes moving the first reader to a next y-position,e.g., for performing further y-position measurements at a differenty-position than the immediately previous y-position.

In one approach, the next y-position corresponds to an averagey-position of the second reader during the immediately previousmeasuring. Accordingly, in such an approach, a distance between the nexty-position and the average y-position of the second reader during theimmediately previous measuring may about equal the distance between thefirst and second readers in a direction perpendicular to the tape traveldirection thereacross.

In another approach, the next y-position corresponds to a predefinedstep size away from the y-position of the first reader during theimmediately previous measuring. In various approaches, the predefinedstep may include any distance. In some approaches, the predefined stepis less than or equal to the distance between the first and secondreaders in a direction perpendicular to the tape travel directionthereacross. In other approaches, the predefined step is greater thedistance between the first and second readers in a directionperpendicular to the tape travel direction thereacross.

In one approach, after the first reader is moved to the next y-position,y-positions of the second reader while the first reader is at the nexty-position are measured in operation 912, e.g., in a similar manner asperformed in operation 906.

In another approach, the y-positions measured by the second reader whilethe first reader is at the next y-position are averaged in operation914, e.g., in a similar manner as performed in operation 908.

It should be noted that the process defined by operations 910-914 may beperformed any number of times, and preferably several times, e.g., see“Repeat process several times” logic exiting operation 914 and loopingback to operation 910. Performing more iterations tends to result in amore accurate nonlinearity characterization of the measured servopatterns of the servo band, as will become apparent in operation 916. Inone approach, the process (operations 910-914) stops when an end of theservo band is reached. For example, in one approach, upon detecting thatthe next y-position resides on an outermost portion of the servo bandand/or off of the servo band, the process stops. Accordingly, they-position measurements may correlate to different y-positions acrossthe entire servo band, e.g., from the first position of the secondreader to the last position of the second reader (where the processends).

Operation 916 includes calculating a unique nonlinearity value of theservo pattern in the servo band for each of the average y-positionvalues using the respective average y-position value.

In one approach, calculating a unique nonlinearity value of the servopattern in the servo band for each of the average y-position valuesincludes calculating a difference between the average y-position valuesand linearized y-positions. To clarify, in some approaches, the “averagey-position” corresponds to an (average) measured y-position, i.e. they-position based on measured Ai counts and computed by means of Equation1, which assumes a linear servo pattern. In such an approach, thelinearized y-positions corresponds to where the y-position is expectedto be. Accordingly, y-positions having a relatively greater differencebetween an average y-position value and a linearized y-positions may beassumed to correspond to and thereby contribute to greater degrees ofnonlinearity in the servo band. In contrast, y-positions having arelatively lesser difference between an average y-position value and alinearized y-positions may be assumed to contribute less, if at all, tononlinearity in measured servo patters.

In various approaches, the linearized y-positions are calculated basedon an assumption of at least two y-positions. In preferred approaches,the at least two y-positions are known and/or assumed to be accurate.For example, in one approach, the linearized y-positions are calculatedbased on the first y-position and the last average measured y-position.In such an approach the first y-position and the last average measuredy-position may serve as anchor points.

Accordingly, in one approach, each of the linearized y-positionscorrespond to a different position along a linear function that extendsbetween the first y-position and the last average measured y-position,e.g., see FIG. 11A.

Moreover, in some approaches, the calculated unique nonlinearity valuesare stored and/or output, e.g., see operation 918. According to oneapproach, the calculated unique nonlinearity values are stored in and/oroutput to a table of nonlinearity values. According to another approach,the calculated unique nonlinearity values are additionally and/oralternatively stored and/or output to a controller for use incompensating for the calculated nonlinearity of the servo pattern in theservo band, e.g., as will be described elsewhere herein (see FIG. 16).

It should be noted that the number of servo frames used during variousoperations of method 900 may depend on the amount of tape that is passedby the head during such operations. In some approaches, at least onemeter of tape is passed over the head in at least one of the measuringoperations. In other approaches, at least fifty meters of tape is passedover the head in at least one of the measuring operations. In yetanother approach, at least one hundred meters of tape is passed over thehead in at least one of the measuring operations. Accordingly, suchmeasuring operations may be performed using any number of servo frames,e.g., at least one, hundreds, thousands, etc.

It should be noted that the greater the number of incorporated servoframes, the greater the accuracy of characterizing nonlinearity may be.This is because nonlinearities are often on the nanometer scale, andtherefore more samples should provide a more accurate reflection of evena nanometer increment of nonlinearity.

It should also be noted that according to various approaches, method 900may be performed at any time and/or any number of times. For example, inone approach, method 900 is performed on a magnetic tape duringmanufacturing. In such an approach, the nonlinearity of servo patternsof the magnetic tape are characterized (if any nonlinearity exists) andstored in a memory component of the cartridge that contains the magnetictape. According to another approach, method 900 is additionally and/oralternatively performed on a magnetic tape, e.g., on demand, uponrequest from a host or library controller, in response to detecting thatthe magnetic tape has been loaded in a tape drive, etc. According to yetanother approach, method 900 is additionally and/or alternativelyperformed, e.g., by a tape drive, at any time after the magnetic tape isloaded into the tape drive, e.g., in response to detecting servoingerrors.

Accordingly, as a result of characterizing such nonlinearities of servopatterns, writing and/or reading events may utilize suchcharacterizations for mitigating writing and/or readback errors thatwould otherwise occur in response to treating nonlinear servo patternsas if they were linear. Utilizing such characterizations will bedescribed in detail elsewhere herein, e.g., see FIG. 16.

FIG. 10A-10B depict a representation 1000 of starting and endingy-positions of a magnetic tape head relative to a servo pattern in aservo band, e.g., when performing the method of FIG. 9, in accordancewith one embodiment. As an option, the present representation 1000 maybe implemented in conjunction with features from any other embodimentlisted herein, such as those described with reference to the other FIGS.Of course, however, such representation 1000 and others presented hereinmay be used in various applications and/or in permutations which may ormay not be specifically described in the illustrative embodiments listedherein. Further, the representation 1000 presented herein may be used inany desired environment.

Referring first to FIG. 10A, representation 1000 includes a servo band1002, which includes a TBS pattern 1004 having nonlinear stripes.Moreover, representation 1000 includes a magnetic tape head 1006, havinga first reader 1008 and a second reader 1010. The magnetic tape head1006 is skewed for misaligning the first and second readers 1008, 1010in a direction perpendicular to a tape travel direction 1012 thereacrossby a predefined distance 1018. The skew is preferably static, i.e.,remains fixed during the procedure as the head transitions from theposition shown in FIG. 10A to that shown in FIG. 10B.

In FIG. 10A, the first reader 1008 is shown positioned at a firsty-position 1014 relative to the TBS pattern 1004 in the servo band 1002,and the second reader 1010 is shown positioned at a second y-position1016 relative to the TBS pattern 1004 in the servo band 1002. In oneapproach, the first reader 1008 is positioned, e.g., as in operation 904of FIG. 9, and further operations such as 906 and 908 of FIG. 9 may beperformed.

As described elsewhere herein, e.g., see operation 910 of method 900, inone approach, the first reader 1008 is moved to a next y-position formeasuring y-positions of the second reader. For example, in oneapproach, the next y-position corresponds to an average y-position ofthe second reader during the immediately previous measuring, e.g.,position 1016 of FIG. 10A after the first reading operation. Accordingto another approach, the next y-position corresponds to a predefinedstep size away from the y-position of the first reader during theimmediately previous measuring.

Referring now to FIG. 10B, after potentially several operations such asan iteration of operations 910-914 of FIG. 9, the first reader 1008 isshown positioned on a final y-position 1020, and the second reader 1010is shown positioned on a final y-position 1022. In one approach, thefinal y-positions 1020, 1022 of the first and second readers 1008, 1010(respectively) correspond to an end of the servo band 1002 beingreached, a predefined y-position, etc. Accordingly, the final y-position1022 may be the final y-position measured by the second reader.

In one approach, some or all of the y-positions measured by the secondreader are averaged, e.g., as in operation 914 of FIG. 9. Accordingly,in one approach, a unique nonlinearity value of the servo pattern in theservo band for each of the average y-position values are calculatedusing the respective average y-position value. Such unique nonlinearityvalue of the servo pattern in the servo band may be stored and/oroutput.

FIG. 11A-11B depict graphs 1100, 1150, in accordance with variousembodiments. As an option, the present graphs 1100, 1150 may beimplemented in conjunction with features from any other embodimentlisted herein, such as those described with reference to the other FIGS.Of course, however, such graphs 1100, 1150 and others presented hereinmay be used in various applications and/or in permutations which may ormay not be specifically described in the illustrative embodiments listedherein. Further, the graphs 1100, 1150 presented herein may be used inany desired environment.

Referring now to FIG. 11A, graph 1100 plots average measured y-positions{tilde over (y)}_(i), e.g., y₀ ⁽¹⁾, y₀ ⁽²⁾, y₁ ⁽²⁾, y₂ ⁽²⁾ (wheresuperscript (1) denotes the first reader, (2) denotes the second reader,and the subscript denotes the number of the read operation in a sequenceof read operations), and y₃ ⁽²⁾ vs. linearized y-positions y_(i), e.g.,y₀, y₁, y₂, y₃, y₄. For reference, the measured y-position y₀ ⁽¹⁾represents the first y-position that the first reader is positioned atrelative to a servo pattern in a servo band. Moreover, the measuredy-position y₃ ⁽²⁾ represents the last average y-position that the secondreader measures at. Accordingly, each of the measured y-positions y₀⁽²⁾, y₁ ⁽²⁾, y₂ ⁽²⁾ reflect the positions at which the second readermeasures the servo pattern, and the first reader follows, whileperforming the process introduced elsewhere herein, e.g., see operations910-914 of method 900.

A measured y-position line 1104 connects each of the measuredy-positions {tilde over (y)}_(i), and an linearized y-position line 1102connects each of the linearized y-positions y_(i).

In one approach, based on calculating N number of linearized y-positionsy_(i) of the servo band is calculated based on a first y-position y₀=y₀⁽¹⁾ and a last y-position, e.g., y_(N)=y_(N-1) ⁽²⁾, i.e. based on themeasured y-positions y₀ ⁽¹⁾ and y_(N-1) ⁽²⁾. Accordingly, in oneapproach, the following Equation (2) is used for calculating thelinearized y-positions y_(i):

y _(i) =y ₀ −p*i  Equation (2)

where i=0 . . . N, and p=(y₀−y_(N))/N.

Moreover, in one approach, the measured y-positions is determined usingthe following Equations (3):

{tilde over (y)} _(i) =y _(i) ⁽¹⁾ for 0≤i<N,

{tilde over (y)} _(i) =y _(N-1) ⁽²⁾ for i=N.  Equation (3)

Accordingly, in one approach, calculating a unique nonlinearity value ofthe servo pattern in the servo band for each of the average y-positionvalues includes calculating a difference between the average y-positionvalues and linearized y-positions. For example, with continued referenceto FIG. 11A, in one approach a unique nonlinearity value e_(i) of theservo pattern in the servo band for each of the average y-positionvalues is calculated using the following Equation (4):

$\begin{matrix}{\quad\begin{matrix}{e_{i} = {{\overset{\sim}{y}}_{i} - y_{i}}} & {{{{for}\mspace{14mu} 0} < i < N},} \\0 & {{else}.}\end{matrix}} & {{Equation}\mspace{14mu} (4)}\end{matrix}$

In other words, as illustrated in FIG. 11A, unique nonlinearity valuese₁, e₂, and e₃ illustrate the difference between the average y-positionvalues y₀ ⁽²⁾, y₁ ⁽²⁾, y₂ ⁽²⁾, and the linearized y-positions y₁, y₂, y₃(respectively).

It should be noted that in one approach, measured y-positions y₀ ⁽²⁾, y₁⁽²⁾, y₂ ⁽²⁾ represent y-positions that are traversed by both a first anda second reader of a skewed magnetic tape head when the step size isequal to the lateral offset of the first and second readers (e.g., 1018of FIG. 10A), and therefore such measured y-positions also include axislabels y₁ ⁽¹⁾, y₂ ⁽¹⁾, and y₃ ⁽¹⁾. Moreover, the measured y-positions y₀⁽¹⁾ may only be traversed by the first reader of the skewed magnetictape head, and the y-position y₃ ⁽²⁾ may only be traversed by the secondreader of the skewed magnetic tape head (e.g., see the first y-position1014 and the final y-position 1022 of FIGS. 10A-10B), and therefore suchmeasured y-positions each only include a single axis label.

In the present approach, a unique nonlinearity value of the servopattern in the servo band is calculated for each of the averagey-position values using different respective average y-position valuesmeasured by a second reader of a skewed magnetic tape head. Of course,such respective average y-positions of the second reader relative to theservo pattern in the servo band may be measured while the first readeris at a different y-position, e.g., see the first y-position and/or thenext y-position of method 900.

In one approach, where the next y-position corresponds to a predefinedstep size away from the y-position of the first reader during theimmediately previous measuring, the skew applied to the magnetic tapehead preferably spaces the first and second readers about an estimatedvalue of p (see Equation 2) apart in a direction perpendicular to a tapetravel direction thereacross. In one approach, provided that the skewapplied to the magnetic tape head spaces the first and second readersless than or about an estimated value of p apart from each other, thepredefined step size is set to be the estimated value of p. Put adifferent way, the skew applied to the head is preferably chosen suchthat on average y_(i) ⁽¹⁾−y_(i) ⁽²⁾≈p or equivalently Σ_(i=0:N-1)(y_(i)⁽¹⁾−y_(i) ⁽²⁾)=Np. Accordingly, in one approach, the y-position of thefirst reader is adjusted to the predefined step size away from theimmediately previous measuring in each step sequence.

Referring now to FIG. 11B, graph 1150 depicts the measured y-positions{tilde over (y)}_(i), e.g., y₀ ⁽¹⁾, y₀ ⁽²⁾, y₁ ⁽²⁾, y₂ ⁽²⁾, and y₃ ⁽²⁾vs. the calculated unique nonlinearity value of the servo pattern in theservo band for each of the average y-position values.

FIG. 12-13 include graphs 1200, 1300 which plot measured y-positions vs.unique nonlinearity values of servo patterns in two different servobands (respectively), in accordance with various embodiments. As anoption, the present graphs 1200, 1300 may be implemented in conjunctionwith features from any other embodiment listed herein, such as thosedescribed with reference to the other FIGS. Of course, however, suchgraphs 1200, 1300 and others presented herein may be used in variousapplications and/or in permutations which may or may not be specificallydescribed in the illustrative embodiments listed herein. Further, thegraphs 1200, 1300 presented herein may be used in any desiredenvironment.

Referring first to FIG. 12, graph 1200 illustrates nonlinearities of TBSpatterns in a first servo band on a magnetic tape, which were measuredand characterized in experimental testing. Specifically, the graph 1200includes a measured y-position (nm) vs. pattern nonlinearity (nm)comparison of three different readings, e.g., reflected by nonlinearityprofiles 1202, 1204, 1206, performed using operations of method 900,performed at three different points in time. The small differences inthe nonlinearity profiles 1202, 1204, 1206 reflect measurement noise andsmall skew drift. Moreover, it should be noted that in the presentapproach, the three measurements incorporate all of the servo stripes ofthe measured servo frames. For example, in the context of the TBSpattern 1004 of FIGS. 10A-10B, all stripes in the A and C bursts arewritten with the same servo write gap (i.e. a first write gap), so theyare expected to have the same nonlinearity. Similarly, all stripes inthe B and D burst are written with the same servo write gap (i.e. thesecond write gap), so they are expected to have the same nonlinearity.Moreover, the first and second write gap are expected to have differentnonlinearities, but since the A_(i) count measurement is between A and Bburst stripes (or between C and D burst stripes), only a single patternnonlinearity is measured.

With continued reference to FIG. 12, in the current approach, due to alack of having an absolute measurement reference, it may be assumed thata distance between the first measured y-position and the final measuredy-position spans 88.31 μm in total, e.g., 43 μm above a servo centerlineof the servo band and 45.31 μm below the servo centerline of the servoband. Moreover, anchor points of the measured y-position are designatedas residing on a zero of the nonlinearity spectrum, i.e. these anchorpoint are assumed to have no nonlinearity error. These anchor points areassumed to reside on a linear portion of the servo band.

Accordingly, the first measured y-position may be located about 43 μmabove the servo centerline. Moreover, the end of the servo band (45.31μm below the centerline of the servo band) may be the last measuredy-position.

In the current example, the lateral offset distance between a firstreader and a second reader (in the direction perpendicular to a tapetravel direction thereacross, e.g., 1018 of FIG. 10A) of the magnetictape head used to measure such y-positions is about 4.205 μm. Thisdistance may also be calculated by dividing the sample distance 88.31 μmby the number times (N) the first reader was moved to a next y-positionfor measuring different y-positions by the second reader. Here assumethat N=21. Accordingly, in the present approach, the distance betweeneach y-position measured by the second reader, and the y-positionpreviously read by the second reader is about 4.205 μm.

For reference, if the stripes of the measured TBS pattern were linear,each of the profiles 1202, 1204, 1206 would not vary from the zero ofthe plotted nonlinearity (nm). However, in graph 1200, the stripes ofthe measured TBS pattern in the servo band may be determined to includenonlinearities. In one approach, negative nonlinearity values correspondto the measured servo y-position being lower (in a directionperpendicular to a tape travel direction thereacross) than they-position would be if the servo stripes written on the magnetic tapehad no nonlinearities. In contrast, in another approach, positivenonlinearity values correspond to the measured servo y-position beinghigher (in a direction perpendicular to a tape travel directionthereacross) than the y-position would be if the servo stripes writtenon the magnetic tape had no nonlinearities.

For purposes of a further example, referring now to FIG. 13, graph 1300illustrates nonlinearities of a second TBS pattern on the same magnetictape as that of FIG. 12. However, it should be noted that the TBSpattern of FIG. 13 resides in a different servo band than the servo bandassociated with the TBS pattern of FIG. 12, although each of the twoservo bands preferably border a common data band.

Graph 1300 illustrates nonlinearities of TBS patterns in a second servoband. Specifically the graph 1300 includes a measured y-position (nm)vs. pattern nonlinearity (nm) comparison of three different readings,e.g., reflected by nonlinearity profiles 1302, 1304, 1306, performedusing the same measurement procedure introduced in method 900, performedat three different points in time. In the present approach, each of thenonlinearity profiles 1302, 1304, 1306 include primarily negativenonlinearity values (other than a first y-position and a last averagemeasured y-position which are assumed to be linear and therefore havenonlinearity values of zero). Accordingly, in one approach, the measuredy-positions corresponding to the current testing sample of graph 1300 islower in a servo band (in a direction perpendicular to a tape traveldirection thereacross) than the y-positions would otherwise be ifwritten on the magnetic tape without nonlinearities.

For reference, from graph 1300 it can be observed that the greatestdegree of nonlinearity exists in the middle of the sampled TBS patterns,e.g., having about a −160 nm characterized pattern nonlinearity.According to various approaches, these characterizations ofnonlinearities are stored and thereby available for future reference,such as to be used in compensating for such nonlinearities, e.g., aswill be described in greater detail elsewhere herein (see method 1600).

FIGS. 14-15B include graphs 1400, 1500, 1550 which plotcharacterizations of nonlinearity, in accordance with variousembodiments. As an option, the present graphs 1400, 1500, 1550 may beimplemented in conjunction with features from any other embodimentlisted herein, such as those described with reference to the other FIGS.Of course, however, such graphs 1400, 1500, 1550 and others presentedherein may be used in various applications and/or in permutations whichmay or may not be specifically described in the illustrative embodimentslisted herein. Further, the graphs 1400, 1500, 1550 presented herein maybe used in any desired environment.

Referring first to FIG. 14, graph 1400 plots differential patternnonlinearity between the TBS pattern of the first servo band sampled inFIG. 12 and the TBS pattern of the second servo band sampled in FIG. 13.Specifically, nonlinearity profile 1402 depicts the differential patternnonlinearity (difference) between the nonlinearity profile 1202 of FIG.12 and the nonlinearity profile 1302 of FIG. 13. Moreover, nonlinearityprofile 1404 depicts the differential pattern nonlinearity (difference)between the nonlinearity profile 1204 of FIG. 12 and the nonlinearityprofile 1304 of FIG. 13. Furthermore, nonlinearity profile 1406 depictsthe differential pattern nonlinearity (difference) between thenonlinearity profile 1206 of FIG. 12 and the nonlinearity profile 1306of FIG. 13.

As discussed above, data is recorded in the regions of tape locatedbetween pairs of servo bands. In read/write heads of state-of-the-arttape drives, two servo readers are normally available per head module.Servo reader 1 then reads the servo band above the data band, whileservo reader 2 simultaneously reads the servo band below the data band.Assume for purposes of an example that ypos₁ and ypos₂ are defined asthe y-positions measured from servo reader 1 and servo reader 2,respectively. Then the delta y-position may be defined as (ypos₁−ypos₂),i.e. the difference between the measured y-position of two servo readerswhich read two servo bands that border a common data band. Referringfirst to FIG. 15A, graph 1500 plots a measured delta y-position 1502(deltaSpan) between servo patterns of the two servo bands sampled inFIG. 12 and FIG. 13. The graph 1500 is the result of actuating a tapehead module such that the modules servo reads are ramping up and down inthe servo bands in a single measurement. As illustrated in FIG. 15A, thedelta y-position 1502 is very noisy. This data may be contrasted withthe differential pattern nonlinearity 1404 from FIG. 14.

Referring first to FIG. 15B, graph 1550 illustrates the differentialpattern nonlinearity 1404 from FIG. 14, and an averaged and smoothedestimate 1552 of the delta y-position obtained from five sequentialcaptures. As illustrated in FIG. 15B, the delta y-position is noisy,although less noisy on average than the delta y-position 1502 of FIG.15A.

The present invention may be a system, a method, and/or a computerprogram product. The computer program product may include a computerreadable storage medium (or media) having computer readable programinstructions thereon for causing a processor to carry out aspects of thepresent invention.

The computer readable storage medium can be a tangible device that canretain and store instructions for use by an instruction executiondevice. The computer readable storage medium may be, for example, but isnot limited to, an electronic storage device, a magnetic storage device,an optical storage device, an electromagnetic storage device, asemiconductor storage device, or any suitable combination of theforegoing. A non-exhaustive list of more specific examples of thecomputer readable storage medium includes the following: a portablecomputer diskette, a hard disk, a random access memory (RAM), aread-only memory (ROM), an erasable programmable read-only memory (EPROMor Flash memory), a static random access memory (SRAM), a portableCD-ROM, a digital versatile disk (DVD), a memory stick, a floppy disk, amechanically encoded device such as punch-cards or raised structures ina groove having instructions recorded thereon, and any suitablecombination of the foregoing. A computer readable storage medium, asused herein, is not to be construed as being transitory signals per se,such as radio waves or other freely propagating electromagnetic waves,electromagnetic waves propagating through a waveguide or othertransmission media (e.g., light pulses passing through a fiber-opticcable), or electrical signals transmitted through a wire.

Computer readable program instructions described herein can bedownloaded to respective computing/processing devices from a computerreadable storage medium or to an external computer or external storagedevice via a network, for example, the Internet, a local area network, awide area network and/or a wireless network. The network may comprisecopper transmission cables, optical transmission fibers, wirelesstransmission, routers, firewalls, switches, gateway computers and/oredge servers. A network adapter card or network interface in eachcomputing/processing device receives computer readable programinstructions from the network and forwards the computer readable programinstructions for storage in a computer readable storage medium withinthe respective computing/processing device.

Computer readable program instructions for carrying out operations ofthe present invention may be assembler instructions,instruction-set-architecture (ISA) instructions, machine instructions,machine dependent instructions, microcode, firmware instructions,state-setting data, or either source code or object code written in anycombination of one or more programming languages, including an objectoriented programming language such as Smalltalk, C++ or the like, andconventional procedural programming languages, such as the “C”programming language or similar programming languages. The computerreadable program instructions may execute entirely on the user'scomputer, partly on the user's computer, as a stand-alone softwarepackage, partly on the user's computer and partly on a remote computeror entirely on the remote computer or server. In the latter scenario,the remote computer may be connected to the user's computer through anytype of network, including a local area network (LAN) or a wide areanetwork (WAN), or the connection may be made to an external computer(for example, through the Internet using an Internet Service Provider).In some embodiments, electronic circuitry including, for example,programmable logic circuitry, field-programmable gate arrays (FPGA), orprogrammable logic arrays (PLA) may execute the computer readableprogram instructions by utilizing state information of the computerreadable program instructions to personalize the electronic circuitry,in order to perform aspects of the present invention.

Aspects of the present invention are described herein with reference toflowchart illustrations and/or block diagrams of methods, apparatus(systems), and computer program products according to embodiments of theinvention. It will be understood that each block of the flowchartillustrations and/or block diagrams, and combinations of blocks in theflowchart illustrations and/or block diagrams, can be implemented bycomputer readable program instructions.

These computer readable program instructions may be provided to aprocessor of a general purpose computer, special purpose computer, orother programmable data processing apparatus to produce a machine, suchthat the instructions, which execute via the processor of the computeror other programmable data processing apparatus, create means forimplementing the functions/acts specified in the flowchart and/or blockdiagram block or blocks. These computer readable program instructionsmay also be stored in a computer readable storage medium that can directa computer, a programmable data processing apparatus, and/or otherdevices to function in a particular manner, such that the computerreadable storage medium having instructions stored therein comprises anarticle of manufacture including instructions which implement aspects ofthe function/act specified in the flowchart and/or block diagram blockor blocks.

The computer readable program instructions may also be loaded onto acomputer, other programmable data processing apparatus, or other deviceto cause a series of operational steps to be performed on the computer,other programmable apparatus or other device to produce a computerimplemented process, such that the instructions which execute on thecomputer, other programmable apparatus, or other device implement thefunctions/acts specified in the flowchart and/or block diagram block orblocks.

The flowchart and block diagrams in the Figures illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods, and computer program products according to variousembodiments of the present invention. In this regard, each block in theflowchart or block diagrams may represent a module, segment, or portionof instructions, which comprises one or more executable instructions forimplementing the specified logical function(s). In some alternativeimplementations, the functions noted in the block may occur out of theorder noted in the figures. For example, two blocks shown in successionmay, in fact, be executed substantially concurrently, or the blocks maysometimes be executed in the reverse order, depending upon thefunctionality involved. It will also be noted that each block of theblock diagrams and/or flowchart illustration, and combinations of blocksin the block diagrams and/or flowchart illustration, can be implementedby special purpose hardware-based systems that perform the specifiedfunctions or acts or carry out combinations of special purpose hardwareand computer instructions.

Moreover, a system according to various embodiments may include aprocessor and logic integrated with and/or executable by the processor,the logic being configured to perform one or more of the process stepsrecited herein. By integrated with, what is meant is that the processorhas logic embedded therewith as hardware logic, such as an applicationspecific integrated circuit (ASIC), a field programmable gate array(FPGA), etc. By executable by the processor, what is meant is that thelogic is hardware logic; software logic such as firmware, part of anoperating system, part of an application program; etc., or somecombination of hardware and software logic that is accessible by theprocessor and configured to cause the processor to perform somefunctionality upon execution by the processor. Software logic may bestored on local and/or remote memory of any memory type, as known in theart. Any processor known in the art may be used, such as a softwareprocessor module and/or a hardware processor such as an ASIC, a FPGA, acentral processing unit (CPU), an integrated circuit (IC), etc.

It will be clear that the various features of the foregoing systemsand/or methodologies may be combined in any way, creating a plurality ofcombinations from the descriptions presented above.

It will be further appreciated that embodiments of the present inventionmay be provided in the form of a service deployed on behalf of acustomer.

The inventive concepts disclosed herein have been presented by way ofexample to illustrate the myriad features thereof in a plurality ofillustrative scenarios, embodiments, and/or implementations. It shouldbe appreciated that the concepts generally disclosed are to beconsidered as modular, and may be implemented in any combination,permutation, or synthesis thereof. In addition, any modification,alteration, or equivalent of the presently disclosed features,functions, and concepts that would be appreciated by a person havingordinary skill in the art upon reading the instant descriptions shouldalso be considered within the scope of this disclosure.

While various embodiments have been described above, it should beunderstood that they have been presented by way of example only, and notlimitation. Thus, the breadth and scope of an embodiment of the presentinvention should not be limited by any of the above-described exemplaryembodiments, but should be defined only in accordance with the followingclaims and their equivalents.

1. A method, comprising: applying a static head skew to a magnetic tapehead for misaligning first and second readers in a directionperpendicular to a tape travel direction thereacross; positioning thefirst reader at a first y-position relative to a servo pattern in aservo band; measuring y-positions of the second reader relative to theservo pattern in the servo band while the first reader is at the firsty-position; calculating a y-position value for the second reader basedon the measured y-positions; repeating the following process severaltimes: moving the first reader to a next y-position, measuringy-positions of the second reader while the first reader is at the nexty-position, and calculating a y-position value of the second readerbased on the measured y-position of the second reader while the firstreader is at the next y-position; calculating a unique nonlinearityvalue of the servo pattern in the servo band for each of the calculatedy-position values of the second reader using the respective calculatedy-position value of the second reader; and storing and/or outputting thecalculated nonlinearity values.
 2. The method as recited in claim 1,wherein the next y-position corresponds to an average y-position of thesecond reader during the immediately previous measuring.
 3. The methodas recited in claim 1, wherein calculating a unique nonlinearity valueof the servo pattern in the servo band for each of the calculatedy-position values of the second reader includes calculating a differencebetween the respective calculated y-position value of the second readerand a corresponding linearized y-position.
 4. The method as recited inclaim 3, wherein the linearized y-positions are calculated based on thefirst y-position of the first reader and a last calculated y-positionvalue of the second reader.
 5. The method as recited in claim 4, whereineach of the linearized y-positions correspond to a different positionalong a linear function that extends between the first y-position of thefirst reader and the last calculated y-position value of the secondreader.
 6. The method as recited in claim 1, wherein the process stopswhen an end of the servo band is reached.
 7. The method as recited inclaim 1, wherein the next y-position corresponds to a predefined stepsize from the y-position of the first reader during the immediatelyprevious measuring.
 8. The method as recited in claim 1, where the servopattern is a timing-based servo (TBS) pattern that comprises bursts ofservo stripes, or a high-density (HD) servo pattern containing multipleHD tracks having a repeating periodic waveform.
 9. A computer programproduct for characterizing nonlinearity in a timing-based servo pattern,the computer program product comprising a computer readable storagemedium having program instructions embodied therewith, the programinstructions readable and/or executable by a controller to cause thecontroller to: apply, by the controller, a static head skew to amagnetic tape head for misaligning first and second readers in adirection perpendicular to a tape travel direction thereacross;position, by the controller, the first reader at a first y-positionrelative to a servo pattern in a servo band; measure, by the controller,y-positions of the second reader relative to the servo pattern in theservo band while the first reader is at the first y-position; calculate,by the controller, a y-position value for the second reader based on themeasured y-positions; repeat, by the controller, the following processseveral times: move, by the controller, the first reader to a nexty-position, measure, by the controller, y-positions of the second readerwhile the first reader is at the next y-position, and calculate, by thecontroller, a y-position value of the second reader based on themeasured y-position of the second reader while the first reader is atthe next y-position; calculate, by the controller, a unique nonlinearityvalue of the servo pattern in the servo band for each of the calculatedy-position values of the second reader using the respective calculatedy-position value of the second reader; and store and/or output, by thecontroller, the calculated nonlinearity values.
 10. The computer programproduct as recited in claim 9, wherein the next y-position correspondsto an average y-position of the second reader during the immediatelyprevious measuring.
 11. The computer program product as recited in claim9, wherein calculating a unique nonlinearity value of the servo patternin the servo band for each of the calculated y-position values of thesecond reader includes calculating a difference between the respectivecalculated y-position value of the second reader and a correspondinglinearized y-position.
 12. The computer program product as recited inclaim 11, wherein the linearized y-positions are calculated based on thefirst y-position of the first reader and a last calculated y-positionvalue of the second reader.
 13. The computer program product as recitedin claim 12, wherein each of the linearized y-positions correspond to adifferent position along a linear function that extends between thefirst y-position of the first reader and the last calculated y-positionvalue of the second reader.
 14. The computer program product as recitedin claim 9, wherein the process stops when an end of the servo band isreached.
 15. The computer program product as recited in claim 9, whereinthe next y-position corresponds to a predefined step size from they-position of the first reader during the immediately previousmeasuring.
 16. The computer program product as recited in claim 9,wherein the servo pattern is a timing-based servo (TBS) pattern thatcomprises bursts of servo stripes, or a high-density (HD) servo patterncontaining multiple HD tracks having a repeating periodic waveform. 17.An apparatus, comprising: a controller configured to: apply a statichead skew to a magnetic tape head for misaligning first and secondreaders in a direction perpendicular to a tape travel directionthereacross; position the first reader at a first y-position relative toa servo pattern in a servo band; measure y-positions of the secondreader relative to the servo pattern in the servo band while the firstreader is at the first y-position; calculate a y-position value for thesecond reader based on the measured y-positions; repeat the followingprocess several times: move the first reader to a next y-position,measure y-positions of the second reader while the first reader is atthe next y-position, and calculate a y-position value of the secondreader based on the measured y-position of the second reader while thefirst reader is at the next y-position; calculate a unique nonlinearityvalue of the servo pattern in the servo band for each of the calculatedy-position values of the second reader using the respective calculatedy-position value of the second reader; and store and/or output thecalculated nonlinearity values.
 18. The apparatus as recited in claim17, wherein the next y-position corresponds to an average y-position ofthe second reader during the immediately previous measuring.
 19. Theapparatus as recited in claim 17, wherein calculating a uniquenonlinearity value of the servo pattern in the servo band for each ofthe calculated y-position values of the second reader includescalculating a difference between the respective calculated y-positionvalue of the second reader and a corresponding linearized y-position.20. The apparatus as recited in claim 19, wherein the linearizedy-positions are calculated based on the first y-position of the firstreader and a last calculated y-position value of the second reader.